Question

The half-life of a first order reaction is 1386 s. The rate constant \(k\) is:

• A. \(5 \times 10^{-4}\ \text{s}^{-1}\)
• B. \(2 \times 10^{-4}\ \text{s}^{-1}\)
• C. \(1 \times 10^{-3}\ \text{s}^{-1}\)
• D. \(4 \times 10^{-3}\ \text{s}^{-1}\)

Hint:

For first order reactions: \[ t_{1/2} \propto \frac{1}{k} \] Half-life is independent of initial concentration.

Answer 1

The Correct Option is A

Concept: For a first order reaction: \[ t_{1/2} = \frac{0.693}{k} \] where:

• \(t_{1/2}\) = half-life
• \(k\) = rate constant

Step 1: Write the formula. \[ k = \frac{0.693}{t_{1/2}} \]

Step 2: Substitute the given value. \[ k = \frac{0.693}{1386} \] \[ k = 5 \times 10^{-4}\ \text{s}^{-1} \]

Step 3: Final answer. \[ \boxed{ 5 \times 10^{-4}\ \text{s}^{-1} } \]